## How to Find a Fast Floating-Point atan2 Approximation

Context Over a short period of time, I came across nearly identical approximations of the two parameter arctangent function, atan2, developed by different companies, in different countries, and even in different decades. Fascinated with how the coefficients used in these approximations were derived, I set out to find them. This atan2 implementation is based around a rational approximation of arctangent on the domain -1 to 1:

## Wavelets I - From Filter Banks to the Dilation Equation

This is the first in what I hope will be a series of posts about wavelets, particularly about the Fast Wavelet Transform (FWT). The FWT is extremely useful in practice and also very interesting from a theoretical point of view. Of course there are already plenty of resources, but I found them tending to be either simple implementation guides that do not touch on the many interesting and sometimes crucial connections. Or they are highly mathematical and definition-heavy, for a...

## Amplitude modulation and the sampling theorem

I am working on the 11th and probably final chapter of Think DSP, which follows material my colleague Siddhartan Govindasamy developed for a class at Olin College.  He introduces amplitude modulation as a clever way to sneak up on the Nyquist–Shannon sampling theorem.

Most of the code for the chapter is done: you can check it out in this IPython notebook.  I haven't written the text yet, but I'll outline it here, and paste in the key figures.

Convolution...

## How to build a test environment for audio DSP code in C using GNU/Linux

This may be useful for people that want to try audio DSP algorithms in C.

You will need:

Hardware: You will need regular a PC (not older than a Pentium 3) or small PC will do the job. Sound card: This PC should have a soundcard, at least with one mic input and one headphones output. I/O: You will need, speakers or headphones and a microphone, or some cable the connect the source of the sound to the PC that will be doing the audio processing. Software: You will need a GNU/Linux...

## Wavelets II - Vanishing Moments and Spectral Factorization

October 11, 2016

In the previous blog post I described the workings of the Fast Wavelet Transform (FWT) and how wavelets and filters are related. As promised, in this article we will see how to construct useful filters. Concretely, we will find a way to calculate the Daubechies filters, named after Ingrid Daubechies, who invented them and also laid much of the mathematical foundations for wavelet analysis.

Besides the content of the last post, you should be familiar with basic complex algebra, the...